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yan [13]
2 years ago
13

In a sample of 388 people in a certain, 22% had red hair. Find a 99% confidence interval for the proportion of people in the cou

ntry that have red hair.
Mathematics
1 answer:
Anit [1.1K]2 years ago
8 0

Answer: (0.1658, 0.2742)

Step-by-step explanation:

Formula to find the confidence interval for population proportion is given by :-

\hat{p}\pm z^*\sqrrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where  n= sample size

z*= Critical value

\hat{p} = sample proportion.

As per given , we have

Significance level : \alpha=1-0.99=0.01

According to z-table, Critical value for 99% confidence interval : z*=2.576

Let p be the proportion of people in the country that have red hair.

n= 388

\hat{p}=0.22

Now, required confidence interval for proportion of people in the country that have red hair will be :-

0.22\pm (2.576)\sqrt{\dfrac{0.22(1-0.22)}{388}}

0.22\pm (2.576)\sqrt{0.000442268}

0.22\pm (2.576)(0.02103)

(0.22-0.05417328,\ 0.22+0.05417328 )=(0.16582672,\ 0.27417328)\\\\\approx(0.1658,\ 0.2742)

The 99% confidence interval for the proportion of people in the country that have red hair= (0.1658, 0.2742)

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4. The annual salaries of employees in a large company are approximately
svetoff [14.1K]

a. What percent of people earn less than $40000?

Solution: Let S be the random variable of a salary of employee (in $), S ~ N(50000,20000). Then the random

variable X =−50000

20000

~N(0,1).

( < 40000) = ( <

40000 − 50000

20000 ) = ( < −0.5) = (−0.5) = 0.3085375.

Here Φ(x) denotes the cumulative distribution function of a standard normal distribution.

Answer: 31%.

b. What percent of people earn between $45000 and $65000?

Solution:

(45000 < < 65000) = (

45000 − 50000

20000 < <

65000 − 50000

20000 ) = (−0.25 < < 0.75)

= (0.75) − (−0.25) = 0.7733726 − 0.4012937 = 0.3720789.

Answer: 37%.

c. What percent of people earn more than $70000?

Solution:

( > 70000) = ( >

70000 − 50000

20000 ) = ( > 1) = 0.8413447.

Answer: 84%.

5 0
3 years ago
Write the fraction as a product of a whole number and a unit fraction.<br><br> 7/8
aleksklad [387]
The unit fraction of 7/8 is 1/8
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Evaluate the expression 2x +y for x=7and y=6
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Answer: 20

Step-by-step explanation:

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3 years ago
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Identify an equation in point-slope form for the line perpendicular to
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Answer:

perp. : 1/3= m

y + 8 = 1/3(x -4): answer is c

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8 0
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Suppose the waiting times in an emergency room are normally distributed with a mean (mean) of 40 and a standard deviation (sigma
kipiarov [429]

Answer:

0.68269

Step-by-step explanation:

When we are to find the z score for population where a random sample is picked, the z.score formula we use is

z = (x-μ)/Standard error, where

x is the raw score,

μ is the population mean

Standard error = σ/√n

σ is the population standard deviation

n = random number of samples

For : x = 38 minutes, μ = 40, σ = 10, n = 5

z = 38 - 40/10 /√25

= -2/10/5

= -2/2

= -1

Determining the probability value using z table

P(x = 38) = P(z = -1)

= 0.15866

For : x = 42 minutes, μ = 40, σ = 10, n = 25

z = 42 - 40/10 /√25

= 2/10/5

= 2/2

= 1

Determining the probability value using z table

P(x = 42) = P(z = 1)

= 0.84134

The probability that their average waiting time will be between 38 and 42 minutes is calculated as

P(-Z<x<Z)

= P(-1 < x < 1)

= P(z = 1) - P(z = -1)

= 0.84134 - 0.15866

= 0.68269

Therefore, the probability that their average waiting time will be between 38 and 42 minutes is 0.68269

3 0
3 years ago
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